Adaptive output-feedback stabilisation for hybrid PDE–ODE systems with uncertain input disturbances

ABSTRACT This paper is concerned with the adaptive output-feedback stabilisation for a class of hybrid partial differential equation (PDE)–ordinary differential equation (ODE) systems with uncertain input disturbances. Remarkably, in this paper, only two boundary measurements of the considered system are available for feedback. Moreover, the unknown parameters involved in the system are allowed to belong to an unknown interval. These two aspects make the considered system essentially different from those in the closely related literature. Inspired by the existing results, an observer is first introduced to estimate the unmeasured states of the original system. Then, by adaptive technique and backstepping method, an adaptive output-feedback controller is successfully constructed, which guarantees that the entire closed-loop system is asymptotically stable, and moreover, the parameter estimates converge to their own real values ultimately. Besides, by the semigroup approach, the well-posedness of the entire closed-loop system is achieved. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.